No, they didn't know how to swim. Many of them were either pressed, or "quota men," pulled out of jails and debtor's prisons to serve aboard ship. The bosun's job was to make them obey, by administering on-the-spot corporal punishment.
(Honestly, it is amazing to me that the British Navy could even rule the Channel, with the way their sailors were treated.)
In fact, Jack Aubrey was one of the few sailors who could swim well (unlike Hornblower, who just liked to dance around naked on deck under a seawater pump spray); Jack is noted for diving in and saving over twenty men who have fallen overboard. That doesn't count the number of times he has to dive in to save Maturin.
As for swimming ... I always said I wouldn't get on a boat until I could swim ... but a very large ship might be a blast ...
"The Love Boat. . ."--LOL!
Your account of the British navy reminds me of Mutiny on the Bounty :)